Numerical solution of time-dependent two-dimensional P1 equation of neutron transport

The time-dependent P1 equation for two-dimensional neutron transport is numerically solved by a finite difference approximation of the explicit form along the bicharacteristics of the P1 equation. Applying von Neumann's stability condition to this numerical procedure in an infinite space, we can derive the condition necessary for the solution to be stable. This condition is that the mesh widths satisfy the inequality 0<lambda<=√3/2 with lambda = time mesh Δt/space mesh Δx or Δz, where the time t is measured in units of inverse neutron speed 1/v. The sufficient stability condition on the ratio lambda is to be determined by numerical experiments. It has been found that the upper bound of lambda becomes larger for smaller values of space mesh width. In respect of the stability of numerical solution, the P1 approximation is more advantageous than the diffusion approximation. Transient behavior of neutron flux distribution due to a stationary neutron source is numerically determined assuming zero initial values. After the transient state terminates, the steady state distribution is obtained. (author)